Bobby Valentine was introduced as the new manager of the Red Sox Dec. 1. He boarded a flight to the Dominican Republic the next morning so he personally could tell David Ortiz, then a free agent, how important he was to the team.

Valentine could have used a day to rest. But he needed Ortiz in the middle of his lineup more.

Ortiz had three more hits Sunday and drove in the go-ahead run as the Red Sox beat the Tampa Bay Rays again, 6-4.

That’s three straight victories for the Sox, who will send Daniel Bard to the mound Monday morning seeking a sweep. At 4-5, the Sox are almost fully recovered from their poor first week and sit a game out of first place in the American League East.

It is Ortiz who has led them there. He is 16 of 36 (.444) on the season with seven extra-base hits and 10 RBIs.

“It’s awesome. He’s been having great swings all season,’’ Adrian Gonzalez said. “We’re really feeding off of him.’’

In 2010, Ortiz might have been out of the lineup against a tough lefthander like Tampa Bay’s Matt Moore. He hit .217 against lefthanders in 2009-10, evidence of a hitter in decline.

It got to a point where former manager Terry Francona had no choice but to sit Ortiz or pinch hit for him.

But Ortiz worked diligently to improve his approach against lefties, cutting down on his swing to drive the ball to all fields.

“Lefties are hittable, too,’’ said Ortiz, who is hitting .339 against lefties since the start of the 2011 season. “It all depends what your mind-set is. They throw the ball right over the plate just like righties. You have to take what they give you.’’

Sunday was an example of how far Ortiz has come. He had a double to center field off Moore in the second inning, a single to right in the fourth, and an RBI double to center in the sixth that gave the Red Sox a 5-4 lead.

The second double, off a 94-mile-per-hour fastball, crashed into the wall in center field. It was Ortiz’s seventh hit in as many at-bats, the first time he has done that since 2007.

“Papi is locked in. I can’t even begin to describe it,’’ Rays catcher Chris Gimenez said. “You might as well just walk him the rest of the time.’’

Said Valentine: “I can’t tell if it’s a lefty or a righty. He has the same at-bat from the first inning to the ninth, regardless of who’s throwing, whether it’s soft or hard, in or out. It’s a determined at-bat. When you have that kind of determination, often you have some success and he’s been very successful.’’

Valentine has been impressed with Ortiz since the first day of spring training, noting that he arrived in good shape and wanting to take on more of a leadership role following last season’s collapse.

“The best way to lead is to come up in a big spot and produce,’’ Valentine said. “He’s done that the first 10 days, no doubt about that.’’

The Sox have scored 31 runs in the first three games of the series, hitting seven home runs. Cody Ross and Mike Aviles connected Sunday.

Ross had a three-run shot in the second and Aviles a solo blast to center in the seventh.

Felix Doubront lost a 4-0 lead, giving up three runs in the fifth before Luke Scott homered in the sixth. The lefty was impressive at times, striking out seven. But he also allowed nine hits.

Once Ortiz gave the Red Sox the lead, Scott Atchison, Vicente Padilla, Franklin Morales, and Alfredo Aceves combined for four shutout innings. It was the second save for Aceves.

“I like how we’re looking,’’ Ortiz said. “This is fun.’’

At 36, Ortiz is a well-paid anomaly. Instead of using one player as their primary DH, many teams are rotating players at the position or using low-cost veterans. But for the Red Sox, the old way still works.

“Like a bottle of wine, age is better for David,’’ Kevin Youkilis said. “We have the luxury on this team to have a guy like David. We need him in our lineup.’’

Ortiz just laughs now when he hears speculation that his career is coming to an end.

“I don’t really care what anybody says or what anybody tries to put in my head,’’ he said. “I just go about my business day by day and try my best and let things happen.’’

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